ITERATION OF POLYNOMIAL PAIR UNDER THUE-MORSE DYNAMIC

We study the behavior of a polynomial sequence which is defined by iterating a polynomial pair under Thue-Morse dynamic. We show that in suitable sense, the sequence will behave like {2cos2 n x : n � 1}. Basing on this property we can show that the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian has a common positive lower bound for all coupling.